The SVD System for First-Order Linear Systems


This transient presents theoretical guarantees for stability and performance for the singular price decomposition (SVD) system with subsystems that are linear and 1st order. The SVD system reduces the dimension of the management input. It is used to fulfill the rank-one input constraint imposed by the row-column structure. The row-column structure reduces the amount of inputs needed to manage mn subsystems to m + n. Although the subsystems are linear and initial order, they will be dynamically coupled and are coupled nonlinearly by the SVD of the management input. Thus, the whole system is of order mn and nonlinear. Lyapunov stability and performance analysis demonstrates the result of the SVD dimension reduction through comparisons to a system with full-rank inputs. The analysis conjointly provides convenient strategies for control design. Simulation examples demonstrate the use of the SVD system, theoretical results, and therefore the SVD system's robustness with respect to noise and nonlinearities.

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